The category of Conway games

Several years ago I typed up a rough English translation of André Joyal’s hard-to-find 1977 paper Remarques sur la théorie des jeux à deux personnes, describing the category of Conway games.

My version was on the web server of the University of Manchester mathematics department for a while: I’ve just noticed that it’s not there any more, which is understandable. I’ll put a copy here, in case it’s useful to somebody.

added on 2010-12-29: I’ve updated the file with a version that includes a correction to the definition of the sum of games. Thanks to Glynn in the comments (presumably Glynn Winskel?) for reminding me of this error. Apologies for mistakenly uploading the uncorrected version.

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8 Responses to The category of Conway games

  1. Mike says:

    Hi there,
    Would you mind me referencing your translation? As you mentioned, the original is difficult to find, and so your translation is much appreciated. If this is okay, would you be able to supply me with the necessary information to write a BibTeX entry?


  2. Hi Mike,

    I don’t mind at all.

    I’m not sure what I can give you in the way of bibliographical data; perhaps the best I can do is to quote the footnote on page 1:

    * This paper was published in 1977, in French, in the Gazette des sciences mathématiques du Québec, 1(4), as Remarques sur la Théorie des Jeux à Deux Personnes. The present translation was prepared in April 2003 by Robin Houston. Compiled April 11, 2003.

    I should mention that it’s also unauthorised: although I wrote to Joyal about it in 2003, I never had a reply.

  3. Mike says:

    Thanks Robin,

    It’s much appreciated. You (and your readers) may find the link below interesting, if you haven’t already come across it; it’s a note written for a Novemberfest 2009 talk given by Geoff Cruttwell, expanding on Joyal’s paper.

    Click to access CGCNovTalk.pdf

  4. Glynn says:

    Hi Robin

    Thanks for the translation which I’ve just been reading.

    Isn’t there a mistake in the defn of sum of games H+G? It seems to allow left moves only from H and right moves from G.

    Best wishes


  5. Dear Glynn,

    Yes, indeed! There seems to be a mistake in that definition. Thank you.

    As the Wayback Machine is my witness, I noticed and corrected this in July 2003; but then I accidentally uploaded an older one here.

    For what it’s worth, the error is in Joyal’s original.

    I’ve now found a copy of the corrected version, and uploaded it here to replace the earlier one.

    All the best,

  6. Glynn Winskel says:

    Dear Robin

    Sorry to be slow thanking you for posting the corrected version

    I’ve just sent a message to your old Manchester email address which I hope you can still read – it might be important

    Best wishes


  7. Pingback: Coqで超現実数(1) « ぴらぴら週記

  8. mg1728 says:

    Thanks, I’ve been looking for the original and this is at least as useful!

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